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2 years ago

Perpendicular to the line 2x + 3y = 12, passing through the point (7,3)

Mathematics

1 answer:

Hunter-Best [27]2 years ago

8 0

Answer:

2y-3x+15 = 0

Step-by-step explanation:

let the equation of the perpendicular line: y=mx+c.

Given equation : 2x+3y=12

=> y=-2/3 x+4

so the sope of the equation is m1= -2/3.

as the two lines are mutually perpendicular,

so, m1*m2=-1

=> (-2/3)*m2= -1

=> m2= 3/2

the paerpendicular line : y=(3/2) x+c.

this line pass through (7,3)

so, 3 = (3/2)*7+c

=> c = -15/2

so the perpendicular line y = (3/2)*x -15/2

=> 2y-3x+15 = 0

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The n candidates for a job have been ranked 1, 2, 3,…, n. Let X 5 the rank of a randomly selected candidate, so that X has pmf p

Anon25 [30]

Answer:

A. E(x) = 1/n×n(n+1)/2

B. E(x²) = 1/n

Step-by-step explanation:

The n candidates for a job have been ranked 1,2,3....n. Let x be the rank of a randomly selected candidate. Therefore, the PMF of X is given as

P(x) = {1/n, x = 1,2...n}

Therefore,

Expectation of X

E(x) = summation {xP(×)}

= summation {X×1/n}

= 1/n summation{x}

= 1/n×n(n+1)/2

= n+1/2

Thus, E(x) = 1/n×n(n+1)/2

Value of E(x²)

E(x²) = summation {x²P(×)}

= summation{x²×1/n}

= 1/n

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3 years ago

Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00

Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

$15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88$

So, <em>the principal must be = $8991.88</em>

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3 years ago

The Daily News offers a 15% discount on a Saturday ad that also runs on Tuesday. Skyler Sporting Company contracts for half-page

mart [117]

The ad cost for half page Saturday after discount is

15% of 380 = 0.15×380 = 57
380 - 57 = 323

The ad cost for half page Tuesday after discount is

15% of 330 = 0.15×330 = 49.5
330 - 49.5 = 280.5

Cost of the ads for 10 Saturdays and 10 Tuesdays

(10×323)+(10×280.5) = 3230+2805 = 6035

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3 years ago

Read 2 more answers

What is the slope that passes through the lines (2.1,-4.2) and (2.5,-5)

Usimov [2.4K]

slope = (y2-y1)/(x2-x1)

= (-5--4.2) /(2.5 -2.1)

(-5+4.2)/(2.5-2.1)

=-.8/.4

m=-2

the slope is -2

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